Household alternating current electricity plug-and-play quantum-dot light-emitting diodes

As an intrinsically direct current device, quantum-dot LED cannot be directly driven by household alternating current electricity. Thus, a driver circuit is required, which increases the complexity and cost. Here, by using a transparent and conductive indium-zinc-oxide as an intermediate electrode, we develop a tandem quantum-dot LED that can be operated at both negative and positive alternating current cycles with an external quantum efficiency of 20.09% and 21.15%, respectively. Furthermore, by connecting multiple tandem devices in series, the panel can be directly driven by household alternating current electricity without the need for complicated back-end circuits. Under 220 V/50 Hz driving, the red plug-and-play panel demonstrates a power efficiency of 15.70 lm W−1 and a tunable brightness of up to 25,834 cd m−2. The developed plug-and-play quantum-dot LED panel could enable the production of cost-effective, compact, efficient, and stable solid-state light sources that can be directly powered by household alternating current electricity.

Supplementary Fig. 3 Power efficiency comparison of reported AC driven devices at 1,000 cd m −2 .  Seelso Supplementary Table 1.a, Power efficiency at 1,000 cd m −2 as a function of maximum luminance of AC driven devices.b, Power efficiency at 1,000 cd m −2 as a function of optimal frequency of AC driven devices.
where k e = n e 2π λ ⁄ and n i is the refractive index of i layer.
For the waves to propagate in the i layer, k z,i should be real, which means u<n i /n e .
For example, for the waves to propagate in air, u<1/n e .In the case that k z,i is complex, the waves are evanescent and decrease in amplitude along the z direction.
For the vertical dipole, the power intensity of the generated transverse magnetic (TM) wave at a wavelength of λ and a normalized in-plane wavevector u is: For the horizontal dipole oriented in the plane, the power density of the generated TM and transverse electric (TE) waves at a wavelength of λ and a normalized in-plane wavevector u is: where Re[…] represents the real part of the complex quantity enclosed by brackets.
Note that in some papers 30,31 the K denotes the power density per unit du 2 , and in that case, Eqs. ( 2)-( 4) should be divided by 2u.Also in some papers 32,33 , the signs before the a 1,2 TM and a 1,3 TM are opposite to ours, and this is because we chose a different vector direction when deriving the TM reflection coefficients, as will be discussed later.
In the Eqs.( 2)-( 4), the factor 1±a 12,13 in the numerator describes the wide-angle interference between directly emitted and reflected radiation.The factor 1-a TM,TE in the denominator describes the multiple-beam interference that occurs when the waves are reflected back and forth between region 2 and region 3. Furthermore, a TM,TE =a 1,2 TM,TE a 1,3 TM,TE =r 1,2 TM,TE r 1,3 TM,TE * exp 2jk z,e d where r 1,2 TM,TE and r 1,3 TM,TE are the reflection coefficients of the bottom interface (between region 1 and 2) and the top interface (between region 1 and 3), respectively.
z 1,2 and z 1,3 are the distances of the emitting dipoles from the bottom and the top interfaces, respectively, and d is the thickness of the emitting layer.
For the multiplayer structure with many interfaces, the reflection at each interface should be taken into account.The complex Fresnel reflection coefficients of the interface between i and i+1 layer are Note that the sign of the reflection coefficient in Eq. ( 8) is different with that reported in other papers or textbooks 32,33 .They differ because in this paper, the direction of the electric field (E) vector (Supplementary Fig. 5) of the reflective waves for the TM polarization is opposite to those in most reports 32,33 .Keeping such difference in mind when evaluating the quantities relating to the TM reflection coefficients [for example, Eqs. ( 2), ( 3), ( 5), ( 6)], the same results can be obtained.
Supplementary Fig. 5 The direction of the electric field vector.Sign convention for reflection coefficients in the case for TE and TM polarization.Note that the direction of E vector of the reflective waves of the TM polarization is opposite to those in most reports.
For multiple layers, starting from the outermost layer, the total reflection coefficients of all layers can then be obtained by iteratively calculating For an isotropic dipole distribution, the total spectral power K per unit normalized in-plane wave vector is finally obtained as The total radiated power by the dipole emitter at λ can be obtained by integrating the area under the power dissipation spectrum.
The F is also called as the Purcell factor, which is determined by the device structure.Additionally, we can compute the fractional power coupled to a specific mode by integrating the area under the power dissipation spectrum corresponding to that mode, and then divided it by the total power.
The far field radiation which determines the useful light emission can be calculated by taking the transmittance of the top surface (region 3) into account.For example, the outcoupled power fractions K TMv ' , K TMh ' , K TEh ' , and K ' radiated into the substrate for u<n sub /n e are calculated as where T 1,3 TM,TE denote the energy transmittance of the top surface (region 3) and can be calculated by The transmittance coefficients t 1,3 TM,TE of the top surface (region 3) can be calculated by using the transfer matrix method.
The fractional power coupled into the air for u<1/n e is finally obtained by considering the reflectance R s and the transmittance T s of the interface between glass substrate and air.
where R c is the total reflectance of all device layers.
The total power coupled into the air can then obtained by integrating K out over all directions in the light escape cone: The coupling efficiency can be obtained by At the presence of cavity structure, the exciton radiated decay rate will be modified by the Purcell factor and thus the quantum yield (QY) of the emitter is also modified as η rad, cav (λ)= Fk r Fk r +k nr = Fk r (k r +k nr ) ⁄ (Fk r +k nr ) (k r +k nr ) ⁄ = Fη rad 1-η rad +Fη rad (22)   where k r and k nr are the radiated and the non-radiated decay rates, respectively, and η rad =k r /(k r +k nr ) is the intrinsic emitter quantum yield.
The QY enhancement due to the presence of cavity thus is η rad == F 1-η rad +Fη rad (23)   In the case that the η rad is low, which means the k nr is the dominant transition, the QY of the emitter can be significantly improved since the k r can be effectively accelerated by the cavity.In the case that the η rad is relatively high, meaning k r ≫k nr , the QY enhancement through speedy the k r is marginal.
Considering the modification of the cavity structure on both coupling efficiency and QY of the emitter, the final improvement due to the cavity thus is which normally is larger than η out due to the contribution of higher QY induced by the cavity.For emitter with a lower QY, the η enhancement could be significantly higher than η out .It is more accurate to evaluate the light enhancement efficiency of the structure by using Eq. ( 24).
The external quantum efficiency (EQE) of the device can be obtained by introducing the charge balance efficiency γ η EQE =γη rad,cav η out =γ s pl (λ) where s pl (λ) is the normalized photoluminescence (PL) spectrum of the device which satisfies ∫ s pl (λ)dλ=1 λ max λ min .At low level excitation such that the Auger recombination and Joule heat activated non-radiated recombination could be neglected, the γ can be extracted by fitting the measured EQE with the calculated η EQE .
The above spectral power quantities per unit normalized in-plane wavevector can be converted into the power densities per unit solid angle by using the relation: total far field radiated power= 2πP out (λ,θ)sinθdθ= K out (λ,u)du where θ=arcsin(n e u) is the light emitting angle in air.The angularly dependent spectrum of the device can then be obtained by S(λ,θ)=s pl (λ)P out (λ,θ) By integrating the spectrum density over all wavelength, the angularly dependent emission intensity can be obtained as equation, the integral range for the left and the right integrations is the same, and thus the integral element for the left and the right integrations is also the same.By using the Fresnel relation n 0 sin(θ) =n e sinθ e =n e u K out (λ,u)